Analysis, Probability And Mathematical Physics On Fractals
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A+-m Kernel
AC Circuit
Almost Periodic Jacobi Matrix
Analysis on Fractals
Asymptotic Behavior
Box Dimension
Capacity
Category=PBMX
Coalescence
Compact Space of Homogeneous Type
Complex Dimension
Complex Impedances
Dimension Profile
Dirichlet Form
Discrete Laplacian
Discrete Weighted Graphs
Double Reflected Brownian Motion
Eigenvalue Approximation
Eigenvalue Counting Function
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Finite Element Method
Fourier Series
Fractal Drum
Fractal Measures
Fractal String
Fractal Surfaces
Fractal Transformations
Fractal Zeta Function
Gauge Function
Hardy Space
Harmonic Decomposition
Harmonic Functions
Heat Equation
Hilbert Space
Hyperbolic Graph
Infinite Wave Propagation Speed
Interpolation
Invariant Measure
Isospectral Torus
Iterated Function System
Krein-Feller Operator
KreinAcAEURA"Feller Operator
Krein–Feller Operator
Magnetic Laplacian
Martin Boundary
Multiresolution Analysis
NaA
Naim Kernel
Naım Kernel
Norm Resolvent Convergence
Numerical Approximation
Orthogonal Polynomials
P C F Fractal
P-Energies
Packing Dimension
Parseval Frame
Post Critically Finite Fractal
Potential Theory
Projective Octagasket
Reproducing Kernel
Reversible Random Walk
Riesz Basis
Schrodinger Operator
Self-Similar Measure
Sobolev Spaces
Spectral Asymptotics
Spectral Measures
Spectral Pair
Spectral Projection
Stationary-Increment Stochastic Processes
Stochastic Partial Differential Equation
Sub-Gaussian Heat Kernel Bounds
Tempered Distributions
Trace Theorems
Unitary One-Parameter Group
Wave Equation
Wavelets
Weighted Sobolev Spaces
Product details
- ISBN 9789811215520
- Publication Date: 27 Mar 2020
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.
